| # | P (kip) | Xw (ft) | Yw (ft) | bx (ft) | by (ft) |
|---|
| # | P | X (ft) | Y (ft) | Mean ord. | Contribution | status |
|---|
Each surface CSV has three columns X, Y, Z (header row optional). All lengths are divided by the deck span L.
List each contour's points in path (draw) order and keep a contour's rows contiguous — the app connects points in file order, so this preserves cusps/folds near the peak (WebPlotDigitizer exports this way if you trace one contour at a time).
Mirror about X=0: if you digitize only one half (X≥0 or X≤0), enable it to reflect points across the axis for both interpolation and display.
Import loads into the currently selected deck type & section (replacing existing data). Export saves the loaded surface as Homberg_<deck>_<section>.csv.
Theory & Help · reference material
How the method works, the simplifications behind the charts, and how to drive the tool above — step by step.
Bridge deck slabs are two-way plates, beyond beam theory, and before FEM became widely available, they were solved with the influence surface: a contour map giving the bending moment at one point of the slab for a unit load placed anywhere on it.
Pucher (1951) charted constant-thickness plates. Homberg & Ropers (1965) extended them to real bridge decks of variable thickness and the German live-load model. The method is fast, transparent, and a strong independent check on shell models for local deck bending.
The bending moment at the response point due to a single wheel is obtained by integrating the influence surface over the wheel footprint. The wheel load P is applied as a uniform pressure p = P/A over the footprint area A, and the moment is M = ∬∬A p·η dA = p·V, where V is the volume enclosed between the influence surface η(ξ,ζ) and the zero plane within the footprint boundary.
The original charts are normalized, meaning the charts are drawn in dimensionless coordinates rather than actual dimensions: position is expressed as a fraction of the span L (ξ, ζ = x/L, y/L), and the plotted ordinate η is the bending moment produced by a unit load, per unit of span L. This lets a single chart apply to any slab of the same thickness ratio and support condition, regardless of its actual span — the real moment is recovered by multiplying by the actual load and, where needed, scaling by the actual L.
Performing these calculations by hand is quite tedious. This tool automates the process by subdividing the influence surface into small areas and performing accurate integration to calculate the volume, even where the surface contains a logarithmic singularity at the response point.
Certain simplifications are made in order to use standard influence surface charts developed for single-span slabs: one case with one long edge free and the other fixed (cantilever span), and one case with both long edges fixed (slab between the webs). In the orthogonal direction, the slab is assumed infinite. For the cantilever slab, two cases were analyzed, with the ratio of deck thickness at the root to that at the tip of the overhang, d1:d3 = 2 and d1:d3 = 3. For the deck between webs (fixed–fixed span), three cases were analyzed: one of constant thickness (d5:d3 = 1), and two with a parabolic soffit, d5:d3 = 1.5 and d5:d3 = 2.0.
The influence surfaces were developed for the response points shown in the box-girder figure below. Moments acting about an axis parallel to the longitudinal slab edges — used to design the main transverse deck reinforcement — are m2x, m3x, m4x, and m5x. Moments in the other direction — used to design the longitudinal reinforcement — are m1y, m2y, and m3y.